Discontinuous Galerkin methods for the multi-dimensional Vlasov-Poisson problem

Blanca Ayuso de Dios Centre de Recerca Matematica (CRM), 08193 Bellaterra, Barcelona, Spain Jose A. Carrillo Universitat Autonoma de Barcelona Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1610.25072

Mathematical Models and Methods in Applied Sciences, 22, 1250042, 2012
We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.
Vlasov-Poisson, Discontinuous Galerkin, mixed finite elements
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@inproceedings{blanca2012discontinuous,
  title={Discontinuous Galerkin methods for the multi-dimensional Vlasov-Poisson problem},
  author={Blanca Ayuso de Dios, Jose A. Carrillo, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012110515891382190},
  booktitle={Mathematical Models and Methods in Applied Sciences},
  volume={22},
  pages={1250042},
  year={2012},
}
Blanca Ayuso de Dios, Jose A. Carrillo, and Chi-Wang Shu. Discontinuous Galerkin methods for the multi-dimensional Vlasov-Poisson problem. 2012. Vol. 22. In Mathematical Models and Methods in Applied Sciences. pp.1250042. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012110515891382190.
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